Semi-Infinite Solid Solution Adjusted for Radial Systems Using Time-Dependent Participating Volume-to-Surface Ratio and Simplified Solutions for Finite Solids

Abstract

Time-dependent participating volume-to-surface ratio, V(t)/A, is used to adjust the semi-infinite (SI) solid solutions to the radial systems. In cylinders and spheres, the present “radial” SI sold model extends the domain of the planar model from δ ≪ R to δ ≈ R (δ is transient penetration depth and R is radius). The corresponding increase in the time span is from 0 < Fo < 0.01 to 0 < Fo < 0.06). The erfc series solution for finite solids (FS), which converges rapidly at small values of time, is simplified, by truncating the first term of the solution. For cylinders and spheres, the resulting half-term approximations are far more precise than the planar SI solid solutions.